Abstract

The recently discovered ability of the quantum cascade laser to produce a harmonic frequency comb has attracted new interest in these devices for both applications and fundamental laser physics. In this review we present an extensive experimental phenomenology of the harmonic state, including its appearance in mid-infrared and terahertz quantum cascade lasers, studies of its destabilization induced by delayed optical feedback, and the assessment of its frequency comb nature. A theoretical model explaining its origin as due to the mutual interaction of population gratings and population pulsations inside the laser cavity will be described. We explore different approaches to control the spacing of the harmonic state, such as optical injection seeding and variation of the device temperature. Prospective applications of the harmonic state include microwave and terahertz generation, picosecond pulse generation in the mid-infrared, and broadband spectroscopy.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (1)

M. Piccardo, N. A. Rubin, L. Meadowcroft, P. Chevalier, H. Yuan, J. Kimchi, and F. Capasso, “Mid-infrared two-photon absorption in an extended-wavelength InGaAs photodetector,” Appl. Phys. Lett. 112, 041106 (2018).
[Crossref]

2017 (5)

D. L. Boiko, A. V. Antonov, D. I. Kuritsyn, A. N. Yablonskiy, S. M. Sergeev, E. E. Orlova, and V. V. Vaks, “Mid-infrared two photon absorption sensitivity of commercial detectors,” Appl. Phys. Lett. 111, 171102 (2017).
[Crossref]

N. N. Vukovic, J. Radovanovic, V. Milanovic, and D. L. Boiko, “Low-threshold RNGH instabilities in quantum cascade lasers,” IEEE J. Sel. Top. Quantum Electron. 23, 1–16 (2017).
[Crossref]

D. Kazakov, M. Piccardo, P. Chevalier, T. S. Mansuripur, Y. Wang, F. Xie, C. en Zah, K. Lascola, A. Belyanin, and F. Capasso, “Self-starting harmonic frequency comb generation in a quantum cascade laser,” Nat. Photonics 11, 789–792 (2017).
[Crossref]

M. Rösch, I.-C. Benea-Chelmus, C. Bonzon, M. J. Süess, M. Beck, J. Faist, and G. Scalari, “Broadband monolithic extractor for metal-metal waveguide based terahertz quantum cascade laser frequency combs,” Appl. Phys. Lett. 111, 021106 (2017).
[Crossref]

P. Figueiredo, M. Suttinger, R. Go, E. Tsvid, C. K. N. Patel, and A. Lyakh, “Progress in high-power continuous-wave quantum cascade lasers [Invited],” Appl. Opt. 56, H15–H23 (2017).
[Crossref]

2016 (8)

M. Rösch, G. Scalari, G. Villares, L. Bosco, M. Beck, and J. Faist, “On-chip, self-detected terahertz dual-comb source,” Appl. Phys. Lett. 108, 171104 (2016).
[Crossref]

T. Nagatsuma, G. Ducournau, and C. C. Renaud, “Advances in terahertz communications accelerated by photonics,” Nat. Photonics 10, 371–379 (2016).
[Crossref]

J. Haas and B. Mizaikoff, “Advances in mid-infrared spectroscopy for chemical analysis,” Annu. Rev. Anal. Chem. 9, 45–68 (2016).
[Crossref]

T. S. Mansuripur, C. Vernet, P. Chevalier, G. Aoust, B. Schwarz, F. Xie, C. Caneau, K. Lascola, C.-E. Zah, D. P. Caffey, T. Day, L. J. Missaggia, M. K. Connors, C. A. Wang, A. Belyanin, and F. Capasso, “Single-mode instability in standing-wave lasers: The quantum cascade laser as a self-pumped parametric oscillator,” Phys. Rev. A 94, 63807 (2016).
[Crossref]

G. Villares, S. Riedi, J. Wolf, D. Kazakov, M. J. Süess, P. Jouy, M. Beck, and J. Faist, “Dispersion engineering of quantum cascade laser frequency combs,” Optica 3, 252 (2016).
[Crossref]

N. Vukovic, J. Radovanovic, V. Milanovic, and D. L. Boiko, “Analytical expression for Risken-Nummedal-Graham-Haken instability threshold in quantum cascade lasers,” Opt. Express 24, 26911–26929 (2016).
[Crossref] [PubMed]

M. Yu, Y. Okawachi, A. G. Griffith, M. Lipson, and A. L. Gaeta, “Mode-locked mid-infrared frequency combs in a silicon microresonator,” Optica. 3, 854–860 (2016).
[Crossref]

D. G. Revin, M. Hemingway, Y. Wang, J. W. Cockburn, and A. Belyanin, “Active mode locking of quantum cascade lasers in an external ring cavity,” Nat. Commun. 7, 11440 (2016).
[Crossref] [PubMed]

2015 (4)

2014 (5)

R. L. Tober, J. D. Bruno, S. Suchalkin, and G. Belenky, “Zigzag modes in quantum cascade laser emission spectra,” J. Opt. Soc. Am. B 31, 2399–2403 (2014).
[Crossref]

G. Villares, A. Hugi, S. Blaser, and J. Faist, “Dual-comb spectroscopy based on quantum-cascade-laser frequency combs,” Nat. Commun. 5, 5192 (2014).
[Crossref] [PubMed]

C. R. Petersen, U. Møller, I. Kubat, B. Zhou, S. Dupont, J. Ramsay, T. Benson, S. Sujecki, N. Abdel-Moneim, Z. Tang, and et al., “Mid-infrared supercontinuum covering the 1.4–13.3 μm molecular fingerprint region using ultra-high na chalcogenide step-index fibre,” Nat. Photonics 8, 830–834 (2014).
[Crossref]

C. Maissen, G. Scalari, F. Valmorra, M. Beck, J. Faist, S. Cibella, R. Leoni, C. Reichl, C. Charpentier, and W. Wegscheider, “Ultrastrong coupling in the near field of complementary split-ring resonators,” Phys. Rev. B 90, 205309 (2014).
[Crossref]

J. B. Khurgin, Y. Dikmelik, A. Hugi, and J. Faist, “Coherent frequency combs produced by self frequency modulation in quantum cascade lasers,” Appl. Phys. Lett. 104, 081118 (2014).
[Crossref]

2013 (2)

M. C. Soriano, J. García-Ojalvo, C. R. Mirasso, and I. Fischer, “Complex photonics: Dynamics and applications of delay-coupled semiconductors lasers,” Rev. Mod. Phys. 85, 421–470 (2013).
[Crossref]

A. K. Wójcik, P. Malara, R. Blanchard, T. S. Mansuripur, F. Capasso, and A. Belyanin, “Generation of picosecond pulses and frequency combs in actively mode locked external ring cavity quantum cascade lasers,” Appl. Phys. Lett. 103, 231102 (2013).
[Crossref]

2012 (2)

A. Hugi, G. Villares, S. Blaser, H. C. Liu, and J. Faist, “Mid-infrared frequency comb based on a quantum cascade laser,” Nature. 492, 229–233 (2012).
[Crossref] [PubMed]

J. R. Freeman, J. Maysonnave, N. Jukam, P. Cavalie, K. Maussang, H. E. Beere, D. A. Ritchie, J. Mangeney, S. S. Dhillon, and J. Tignon, “Direct intensity sampling of a modelocked terahertz quantum cascade laser,” Appl. Phys. Lett. 101, 181115 (2012).
[Crossref]

2011 (1)

S. Barbieri, M. Ravaro, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency synthesis,” Nat. Photonics 5, 306–313 (2011).
[Crossref]

2010 (1)

2009 (1)

2008 (3)

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77, 053804 (2008).
[Crossref]

H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, “Gain Recovery Dynamics and Photon-Driven Transport in Quantum Cascade Lasers,” Phys. Rev. Lett. 100, 167401 (2008).
[Crossref] [PubMed]

H. Choi, T. B. Norris, T. Gresch, M. Giovannini, J. Faist, L. Diehl, and F. Capasso, “Femtosecond dynamics of resonant tunneling and superlattice relaxation in quantum cascade lasers,” Appl. Phys. Lett. 92, 122114 (2008).
[Crossref]

2007 (2)

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, M. Troccoli, J. Faist, and F. Capasso, “Coherent instabilities in a semiconductor laser with fast gain recovery,” Phys. Rev. A 75, 031802 (2007).
[Crossref]

P. Del’Haye, A. Schliesser, and O. Arcizet, “Optical frequency comb generation from a monolithic microresonator,” Nature. 450, 1214–1217 (2007).
[Crossref]

2006 (2)

F. Fuchs, B. Kirn, C. Mann, Q. Yang, W. Bronner, B. Raynor, K. Köhler, and J. Wagner, “Spectral tuning and mode competition of quantum cascade lasers studied by time-resolved Fourier transform spectroscopy,” Proc. SPIE 6386, 63860 (2006).
[Crossref]

C. Xia, M. Kumar, O. P. Kulkarni, M. N. Islam, F. L. Terry, M. J. Freeman, M. Poulain, and G. Mazé, “Mid-infrared supercontinuum generation to 4.5 μm in zblan fluoride fibers by nanosecond diode pumping,” Opt. Lett. 31, 2553–2555 (2006).
[Crossref] [PubMed]

2005 (1)

M. Tani, O. Morikawa, S. Matsuura, and M. Hangyo, “Generation of terahertz radiation by photomixing with dual- and multiple-mode lasers,” Semicond. Sci. Technol. 20, S151 (2005).
[Crossref]

1994 (1)

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264, 553–556 (1994).
[Crossref] [PubMed]

1968 (2)

H. Risken and K. Nummedal, “Self-Pulsing in Lasers,” J. Appl. Phys. 39, 4662–4672 (1968).
[Crossref]

R. Graham and H. Haken, “Quantum theory of light propagation in a fluctuating laser-active medium,” Zeitschrift für Physik 213, 420–450 (1968).
[Crossref]

Abdel-Moneim, N.

C. R. Petersen, U. Møller, I. Kubat, B. Zhou, S. Dupont, J. Ramsay, T. Benson, S. Sujecki, N. Abdel-Moneim, Z. Tang, and et al., “Mid-infrared supercontinuum covering the 1.4–13.3 μm molecular fingerprint region using ultra-high na chalcogenide step-index fibre,” Nat. Photonics 8, 830–834 (2014).
[Crossref]

Agrawal, G. P.

G. P. Agrawal, Nonlinear fiber optics (Academic press, 2007).

Amanti, M.

Q. Y. Lu, M. Razeghi, S. Slivken, N. Bandyopadhyay, Y. Bai, W. J. Zhou, M. Chen, D. Heydari, A. Haddadi, R. McClintock, M. Amanti, and C. Sirtori, “High power frequency comb based on mid-infrared quantum cascade laser at λ ∼ 9μm,” Appl. Phys. Lett. 106, 51105 (2015).
[Crossref]

Antonov, A. V.

D. L. Boiko, A. V. Antonov, D. I. Kuritsyn, A. N. Yablonskiy, S. M. Sergeev, E. E. Orlova, and V. V. Vaks, “Mid-infrared two photon absorption sensitivity of commercial detectors,” Appl. Phys. Lett. 111, 171102 (2017).
[Crossref]

Aoust, G.

T. S. Mansuripur, C. Vernet, P. Chevalier, G. Aoust, B. Schwarz, F. Xie, C. Caneau, K. Lascola, C.-E. Zah, D. P. Caffey, T. Day, L. J. Missaggia, M. K. Connors, C. A. Wang, A. Belyanin, and F. Capasso, “Single-mode instability in standing-wave lasers: The quantum cascade laser as a self-pumped parametric oscillator,” Phys. Rev. A 94, 63807 (2016).
[Crossref]

Apfel, M.

Arcizet, O.

P. Del’Haye, A. Schliesser, and O. Arcizet, “Optical frequency comb generation from a monolithic microresonator,” Nature. 450, 1214–1217 (2007).
[Crossref]

Bai, Y.

Q. Y. Lu, M. Razeghi, S. Slivken, N. Bandyopadhyay, Y. Bai, W. J. Zhou, M. Chen, D. Heydari, A. Haddadi, R. McClintock, M. Amanti, and C. Sirtori, “High power frequency comb based on mid-infrared quantum cascade laser at λ ∼ 9μm,” Appl. Phys. Lett. 106, 51105 (2015).
[Crossref]

Bandyopadhyay, N.

Q. Y. Lu, M. Razeghi, S. Slivken, N. Bandyopadhyay, Y. Bai, W. J. Zhou, M. Chen, D. Heydari, A. Haddadi, R. McClintock, M. Amanti, and C. Sirtori, “High power frequency comb based on mid-infrared quantum cascade laser at λ ∼ 9μm,” Appl. Phys. Lett. 106, 51105 (2015).
[Crossref]

Barbieri, S.

H. Li, P. Laffaille, D. Gacemi, M. Apfel, C. Sirtori, J. Leonardon, G. Santarelli, M. Rösch, G. Scalari, M. Beck, J. Faist, W. Hänsel, R. Holzwarth, and S. Barbieri, “Dynamics of ultra-broadband terahertz quantum cascade lasers for comb operation,” Opt. Express 23, 33270–33294 (2015).
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M. Rösch, G. Scalari, G. Villares, L. Bosco, M. Beck, and J. Faist, “On-chip, self-detected terahertz dual-comb source,” Appl. Phys. Lett. 108, 171104 (2016).
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C. Maissen, G. Scalari, F. Valmorra, M. Beck, J. Faist, S. Cibella, R. Leoni, C. Reichl, C. Charpentier, and W. Wegscheider, “Ultrastrong coupling in the near field of complementary split-ring resonators,” Phys. Rev. B 90, 205309 (2014).
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J. R. Freeman, J. Maysonnave, N. Jukam, P. Cavalie, K. Maussang, H. E. Beere, D. A. Ritchie, J. Mangeney, S. S. Dhillon, and J. Tignon, “Direct intensity sampling of a modelocked terahertz quantum cascade laser,” Appl. Phys. Lett. 101, 181115 (2012).
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Belkin, M. A.

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D. Kazakov, M. Piccardo, P. Chevalier, T. S. Mansuripur, Y. Wang, F. Xie, C. en Zah, K. Lascola, A. Belyanin, and F. Capasso, “Self-starting harmonic frequency comb generation in a quantum cascade laser,” Nat. Photonics 11, 789–792 (2017).
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D. G. Revin, M. Hemingway, Y. Wang, J. W. Cockburn, and A. Belyanin, “Active mode locking of quantum cascade lasers in an external ring cavity,” Nat. Commun. 7, 11440 (2016).
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T. S. Mansuripur, C. Vernet, P. Chevalier, G. Aoust, B. Schwarz, F. Xie, C. Caneau, K. Lascola, C.-E. Zah, D. P. Caffey, T. Day, L. J. Missaggia, M. K. Connors, C. A. Wang, A. Belyanin, and F. Capasso, “Single-mode instability in standing-wave lasers: The quantum cascade laser as a self-pumped parametric oscillator,” Phys. Rev. A 94, 63807 (2016).
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Y. Wang and A. Belyanin, “Active mode-locking of mid-infrared quantum cascade lasers with short gain recovery time,” Opt. Express 23, 4173–4185 (2015).
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[Crossref]

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, M. Troccoli, J. Faist, and F. Capasso, “Coherent instabilities in a semiconductor laser with fast gain recovery,” Phys. Rev. A 75, 031802 (2007).
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M. Rösch, I.-C. Benea-Chelmus, C. Bonzon, M. J. Süess, M. Beck, J. Faist, and G. Scalari, “Broadband monolithic extractor for metal-metal waveguide based terahertz quantum cascade laser frequency combs,” Appl. Phys. Lett. 111, 021106 (2017).
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A. K. Wójcik, P. Malara, R. Blanchard, T. S. Mansuripur, F. Capasso, and A. Belyanin, “Generation of picosecond pulses and frequency combs in actively mode locked external ring cavity quantum cascade lasers,” Appl. Phys. Lett. 103, 231102 (2013).
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M. Rösch, G. Scalari, G. Villares, L. Bosco, M. Beck, and J. Faist, “On-chip, self-detected terahertz dual-comb source,” Appl. Phys. Lett. 108, 171104 (2016).
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[Crossref]

A. K. Wójcik, P. Malara, R. Blanchard, T. S. Mansuripur, F. Capasso, and A. Belyanin, “Generation of picosecond pulses and frequency combs in actively mode locked external ring cavity quantum cascade lasers,” Appl. Phys. Lett. 103, 231102 (2013).
[Crossref]

V.-M. Gkortsas, C. Wang, L. Kuznetsova, L. Diehl, A. Gordon, C. Jirauschek, M. A. Belkin, A. Belyanin, F. Capasso, and F. X. Kärtner, “Dynamics of actively mode-locked quantum cascade lasers,” Opt. Express 18, 13616–13630 (2010).
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[Crossref] [PubMed]

H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, “Gain Recovery Dynamics and Photon-Driven Transport in Quantum Cascade Lasers,” Phys. Rev. Lett. 100, 167401 (2008).
[Crossref] [PubMed]

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77, 053804 (2008).
[Crossref]

H. Choi, T. B. Norris, T. Gresch, M. Giovannini, J. Faist, L. Diehl, and F. Capasso, “Femtosecond dynamics of resonant tunneling and superlattice relaxation in quantum cascade lasers,” Appl. Phys. Lett. 92, 122114 (2008).
[Crossref]

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, M. Troccoli, J. Faist, and F. Capasso, “Coherent instabilities in a semiconductor laser with fast gain recovery,” Phys. Rev. A 75, 031802 (2007).
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Carras, M.

T. S. Mansuripur, G. M. de Naurois, W. Metaferia, C. Junesand, S. Lourdudoss, B. Simozrag, M. Carras, and F. Capasso, “Multiple quasi-stable spectral outputs at constant current in a high-power quantum cascade laser,” in “International Quantum Cascade Lasers School and Workshop,” (Policoro (Italy), 2014).

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J. R. Freeman, J. Maysonnave, N. Jukam, P. Cavalie, K. Maussang, H. E. Beere, D. A. Ritchie, J. Mangeney, S. S. Dhillon, and J. Tignon, “Direct intensity sampling of a modelocked terahertz quantum cascade laser,” Appl. Phys. Lett. 101, 181115 (2012).
[Crossref]

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C. Maissen, G. Scalari, F. Valmorra, M. Beck, J. Faist, S. Cibella, R. Leoni, C. Reichl, C. Charpentier, and W. Wegscheider, “Ultrastrong coupling in the near field of complementary split-ring resonators,” Phys. Rev. B 90, 205309 (2014).
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M. Piccardo, N. A. Rubin, L. Meadowcroft, P. Chevalier, H. Yuan, J. Kimchi, and F. Capasso, “Mid-infrared two-photon absorption in an extended-wavelength InGaAs photodetector,” Appl. Phys. Lett. 112, 041106 (2018).
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D. Kazakov, M. Piccardo, P. Chevalier, T. S. Mansuripur, Y. Wang, F. Xie, C. en Zah, K. Lascola, A. Belyanin, and F. Capasso, “Self-starting harmonic frequency comb generation in a quantum cascade laser,” Nat. Photonics 11, 789–792 (2017).
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T. S. Mansuripur, C. Vernet, P. Chevalier, G. Aoust, B. Schwarz, F. Xie, C. Caneau, K. Lascola, C.-E. Zah, D. P. Caffey, T. Day, L. J. Missaggia, M. K. Connors, C. A. Wang, A. Belyanin, and F. Capasso, “Single-mode instability in standing-wave lasers: The quantum cascade laser as a self-pumped parametric oscillator,” Phys. Rev. A 94, 63807 (2016).
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H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, “Gain Recovery Dynamics and Photon-Driven Transport in Quantum Cascade Lasers,” Phys. Rev. Lett. 100, 167401 (2008).
[Crossref] [PubMed]

H. Choi, T. B. Norris, T. Gresch, M. Giovannini, J. Faist, L. Diehl, and F. Capasso, “Femtosecond dynamics of resonant tunneling and superlattice relaxation in quantum cascade lasers,” Appl. Phys. Lett. 92, 122114 (2008).
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D. G. Revin, M. Hemingway, Y. Wang, J. W. Cockburn, and A. Belyanin, “Active mode locking of quantum cascade lasers in an external ring cavity,” Nat. Commun. 7, 11440 (2016).
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T. S. Mansuripur, C. Vernet, P. Chevalier, G. Aoust, B. Schwarz, F. Xie, C. Caneau, K. Lascola, C.-E. Zah, D. P. Caffey, T. Day, L. J. Missaggia, M. K. Connors, C. A. Wang, A. Belyanin, and F. Capasso, “Single-mode instability in standing-wave lasers: The quantum cascade laser as a self-pumped parametric oscillator,” Phys. Rev. A 94, 63807 (2016).
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[Crossref]

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, M. Troccoli, J. Faist, and F. Capasso, “Coherent instabilities in a semiconductor laser with fast gain recovery,” Phys. Rev. A 75, 031802 (2007).
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S. Barbieri, M. Ravaro, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency synthesis,” Nat. Photonics 5, 306–313 (2011).
[Crossref]

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T. S. Mansuripur, C. Vernet, P. Chevalier, G. Aoust, B. Schwarz, F. Xie, C. Caneau, K. Lascola, C.-E. Zah, D. P. Caffey, T. Day, L. J. Missaggia, M. K. Connors, C. A. Wang, A. Belyanin, and F. Capasso, “Single-mode instability in standing-wave lasers: The quantum cascade laser as a self-pumped parametric oscillator,” Phys. Rev. A 94, 63807 (2016).
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[Crossref]

Diehl, L.

V.-M. Gkortsas, C. Wang, L. Kuznetsova, L. Diehl, A. Gordon, C. Jirauschek, M. A. Belkin, A. Belyanin, F. Capasso, and F. X. Kärtner, “Dynamics of actively mode-locked quantum cascade lasers,” Opt. Express 18, 13616–13630 (2010).
[Crossref] [PubMed]

C. Y. Wang, L. Kuznetsova, V. M. Gkortsas, L. Diehl, F. X. Kärtner, M. A. Belkin, A. Belyanin, X. Li, D. Ham, H. Schneider, P. Grant, C. Y. Song, S. Haffouz, Z. R. Wasilewski, H. C. Liu, and F. Capasso, “Mode-locked pulses from mid-infrared quantum cascade lasers,” Opt. Express 17, 12929–12943 (2009).
[Crossref] [PubMed]

H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, “Gain Recovery Dynamics and Photon-Driven Transport in Quantum Cascade Lasers,” Phys. Rev. Lett. 100, 167401 (2008).
[Crossref] [PubMed]

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77, 053804 (2008).
[Crossref]

H. Choi, T. B. Norris, T. Gresch, M. Giovannini, J. Faist, L. Diehl, and F. Capasso, “Femtosecond dynamics of resonant tunneling and superlattice relaxation in quantum cascade lasers,” Appl. Phys. Lett. 92, 122114 (2008).
[Crossref]

C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, M. Troccoli, J. Faist, and F. Capasso, “Coherent instabilities in a semiconductor laser with fast gain recovery,” Phys. Rev. A 75, 031802 (2007).
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[Crossref]

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D. Kazakov, M. Piccardo, P. Chevalier, T. S. Mansuripur, Y. Wang, F. Xie, C. en Zah, K. Lascola, A. Belyanin, and F. Capasso, “Self-starting harmonic frequency comb generation in a quantum cascade laser,” Nat. Photonics 11, 789–792 (2017).
[Crossref]

Faist, J.

M. Rösch, I.-C. Benea-Chelmus, C. Bonzon, M. J. Süess, M. Beck, J. Faist, and G. Scalari, “Broadband monolithic extractor for metal-metal waveguide based terahertz quantum cascade laser frequency combs,” Appl. Phys. Lett. 111, 021106 (2017).
[Crossref]

G. Villares, S. Riedi, J. Wolf, D. Kazakov, M. J. Süess, P. Jouy, M. Beck, and J. Faist, “Dispersion engineering of quantum cascade laser frequency combs,” Optica 3, 252 (2016).
[Crossref]

M. Rösch, G. Scalari, G. Villares, L. Bosco, M. Beck, and J. Faist, “On-chip, self-detected terahertz dual-comb source,” Appl. Phys. Lett. 108, 171104 (2016).
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Hugi, A.

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Li, X.

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M. Yu, Y. Okawachi, A. G. Griffith, M. Lipson, and A. L. Gaeta, “Mode-locked mid-infrared frequency combs in a silicon microresonator,” Optica. 3, 854–860 (2016).
[Crossref]

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A. Hugi, G. Villares, S. Blaser, H. C. Liu, and J. Faist, “Mid-infrared frequency comb based on a quantum cascade laser,” Nature. 492, 229–233 (2012).
[Crossref] [PubMed]

C. Y. Wang, L. Kuznetsova, V. M. Gkortsas, L. Diehl, F. X. Kärtner, M. A. Belkin, A. Belyanin, X. Li, D. Ham, H. Schneider, P. Grant, C. Y. Song, S. Haffouz, Z. R. Wasilewski, H. C. Liu, and F. Capasso, “Mode-locked pulses from mid-infrared quantum cascade lasers,” Opt. Express 17, 12929–12943 (2009).
[Crossref] [PubMed]

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T. S. Mansuripur, G. M. de Naurois, W. Metaferia, C. Junesand, S. Lourdudoss, B. Simozrag, M. Carras, and F. Capasso, “Multiple quasi-stable spectral outputs at constant current in a high-power quantum cascade laser,” in “International Quantum Cascade Lasers School and Workshop,” (Policoro (Italy), 2014).

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[Crossref]

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F. Fuchs, B. Kirn, C. Mann, Q. Yang, W. Bronner, B. Raynor, K. Köhler, and J. Wagner, “Spectral tuning and mode competition of quantum cascade lasers studied by time-resolved Fourier transform spectroscopy,” Proc. SPIE 6386, 63860 (2006).
[Crossref]

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S. Barbieri, M. Ravaro, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency synthesis,” Nat. Photonics 5, 306–313 (2011).
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D. Kazakov, M. Piccardo, P. Chevalier, T. S. Mansuripur, Y. Wang, F. Xie, C. en Zah, K. Lascola, A. Belyanin, and F. Capasso, “Self-starting harmonic frequency comb generation in a quantum cascade laser,” Nat. Photonics 11, 789–792 (2017).
[Crossref]

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A. K. Wójcik, P. Malara, R. Blanchard, T. S. Mansuripur, F. Capasso, and A. Belyanin, “Generation of picosecond pulses and frequency combs in actively mode locked external ring cavity quantum cascade lasers,” Appl. Phys. Lett. 103, 231102 (2013).
[Crossref]

T. S. Mansuripur, G. M. de Naurois, W. Metaferia, C. Junesand, S. Lourdudoss, B. Simozrag, M. Carras, and F. Capasso, “Multiple quasi-stable spectral outputs at constant current in a high-power quantum cascade laser,” in “International Quantum Cascade Lasers School and Workshop,” (Policoro (Italy), 2014).

Matsuura, S.

M. Tani, O. Morikawa, S. Matsuura, and M. Hangyo, “Generation of terahertz radiation by photomixing with dual- and multiple-mode lasers,” Semicond. Sci. Technol. 20, S151 (2005).
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J. R. Freeman, J. Maysonnave, N. Jukam, P. Cavalie, K. Maussang, H. E. Beere, D. A. Ritchie, J. Mangeney, S. S. Dhillon, and J. Tignon, “Direct intensity sampling of a modelocked terahertz quantum cascade laser,” Appl. Phys. Lett. 101, 181115 (2012).
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Mazé, G.

McClintock, R.

Q. Y. Lu, M. Razeghi, S. Slivken, N. Bandyopadhyay, Y. Bai, W. J. Zhou, M. Chen, D. Heydari, A. Haddadi, R. McClintock, M. Amanti, and C. Sirtori, “High power frequency comb based on mid-infrared quantum cascade laser at λ ∼ 9μm,” Appl. Phys. Lett. 106, 51105 (2015).
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M. Piccardo, N. A. Rubin, L. Meadowcroft, P. Chevalier, H. Yuan, J. Kimchi, and F. Capasso, “Mid-infrared two-photon absorption in an extended-wavelength InGaAs photodetector,” Appl. Phys. Lett. 112, 041106 (2018).
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Figures (9)

Fig. 1
Fig. 1 Harmonic and dense multimode states in QCLs. Optical spectrum of a mid-infrared QCL in the harmonic state with a repetition rate of 400 GHz (top), corresponding to 52 skipped longitudinal modes, much greater larger than that of a QCL operating in a dense multimode regime with a repetition rate of 7.7 GHz (bottom). In both cases, the cavity free spectral range is 7.7 GHz.
Fig. 2
Fig. 2 Spectral instability of a mid-infrared QCL at constant current injection. Every few seconds to a few minutes the laser is observed to hop between a dense multimode state (bottom) and a state characterized by families of modes separated from the central mode by a wide spectral gap (top). The laser is operated at 1.40 Jth.
Fig. 3
Fig. 3 Spectral evolution of mid-infrared and THz continuous wave QCLs as the current is increased in the laser. (a)–(c) Mid-infrared QCLs emitting at 9.8 μm, 3.8 μm and 4.6 μm. Spectra reproduced from [7]. (d) Mid-infrared QCL emitting at ≈ 9 μm. Both the occurrence of different laser states (top) and the evolution of the harmonic state via four-wave mixing processes (bottom) are shown. Figure reproduced from [16]. (e) Representative emission spectra observed in the evolution of a THz QCL. Figure adapted from [17]. (f) Mid-infrared QCL emitting at 4.7 μm. Figure reproduced from [18].
Fig. 4
Fig. 4 Spectral evolution of a QCL obtained collecting its spectral output by different schemes. (a) Purely diverging QCL output. (b) QCL output collimated with an off-axis parabolic mirror (OAP). (c) QCL output collimated using a ZnSe lens.
Fig. 5
Fig. 5 Effect of delayed optical feedback on the spectral evolution of a QCL. (a) Set-up used for the control of the feedback level. The length of the optical path between the QCL and the mirror is about 30 cm. Mid-infrared polarizers allow for controlled modulation of feedback power. OAP, off-axis parabolic mirror; BS, beam splitter. (b)–(d) Spectral evolutions measured at different levels of feedback power coupled back into the cavity as normalized to the total output power of the QCL.
Fig. 6
Fig. 6 Assessment of the mode spacing uniformity of the harmonic state. (a) Down-converted harmonic spectrum from the optical to the microwave domain obtained by means of a multiheterodyne technique. The orange trace represents the spectrum averaged over 1000 sweeps of 2 ms. (b),(c) Optical and microwave set-up for the assessment of the comb nature of the harmonic state based on external and self-detection schemes, respectively. BR, beam reducer; ISO, optical isolator; BS, beam splitter; FLIP, flip mirror; NDF, neutral density filter; BP, bandpass filter; LO, local oscillator; A, amplifier; FTIR, Fourier transform infrared spectrometer. (d) Histogram showing the deviation from equidistant spacing of the harmonic state measured with the set-up shown in (c) for a gate time of 10 ms and 402 counts. Inset: histogram obtained with the set-up shown in (b). (e) Fractional frequency stability of the dual-comb system in self-detection mode (squares) versus external detection mode (circles). The self-detected system shows more than an order of magnitude of increase in frequency stability. Figure adapted from [12].
Fig. 7
Fig. 7 Theoretical predictions of harmonic comb operation of a QCL. (a) Net gain predicted by the perturbation theory of harmonic comb formation using the device parameters of an existing mid-infrared QCL, at a pump level 1.1 times above threshold. (b) Corresponding spectral phase of the positive sideband, where both the central mode and negative sideband are given amplitudes that are purely real. Figure adapted from [12].
Fig. 8
Fig. 8 Influence of the QCL operating temperature on the intermodal spacing of the harmonic state. (a) Measured spacing of the harmonic state as a function of temperature. Error bars correspond to the standard deviation obtained repeating the measurement at each temperature over five consecutive current ramp-ups of the laser. (b) Measured threshold of the single-mode instability corresponding to the appearance of the harmonic state (Jharm) normalized to the lasing threshold of the device (Jth).
Fig. 9
Fig. 9 Prospective applications of the harmonic state of QCLs. (a) The self-beating of the widely-spaced harmonic comb can generate microwave and terahertz radiation which may be used for spectroscopy and wireless communication applications. (b) Short pulses of mid-infrared light used in pump-probe spectroscopy experiments. (c) Broadening the spectral coverage of the harmonic state by means of four-wave mixing in a nonlinear waveguide.

Equations (9)

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t ρ ul = ( i ω ul + 1 T 2 ) ρ ul i d E Δ , t Δ = Δ Δ p T 1 2 i d E ( ρ ul ρ ul * ) + D 2 Δ z 2 , z 2 E n 2 c 2 t 2 E = κ d t 2 ( ρ ul + ρ ul * ) ,
E = E 0 cos ( k 0 z ) e i ω 0 t + E + cos ( k + z ) e i ω + t + E cos ( k z ) e i ω t + c . c . , ρ ul = η 0 cos ( k 0 z ) e i ω 0 t + η + cos ( k + z ) e i ω + t + η cos ( k z ) e i ω t , Δ = Δ 0 + Δ 2 cos ( 2 k 0 z ) + Δ + cos ( δ k z ) e i δ ω t + Δ cos ( δ k z ) e i δ ω t + [ Δ 2 + cos ( ( k 0 + k + ) z ) e i δ ω t + Δ 2 cos ( ( k 0 + k ) z ) e i δ ω t + c . c . ] ,
( n 2 ( ω + ) ω + 2 c 2 k + 2 ) = κ d ω + 2 ( [ α + + ] + [ α + e i ϕ ] | E | | E + | ) , ( n 2 ( ω ) ω 2 c 2 k 2 ) = κ d ω 2 ( [ α ] + [ α + e i ϕ ] | E + | | E | ) .
2 n 2 ( ω + ) c 2 g = κ d ω + ( [ α + + ] + [ α + e i ϕ ] | E | | E + | ) , 2 n 2 ( ω ) c 2 g = κ d ω ( [ α ] + [ α + e i ϕ ] | E + | | E | ) .
η + = α + + E + + α + E * , η = α E + α + E + * ,
α + + = d Δ t h δ ω + i / T 2 [ 1 + ( d | E 0 | ) 2 ( T g T 2 + 1 2 ( 1 δ ω + i / T 1 + 1 δ ω + i / T g ) ( 1 δ ω + i / T 2 i T 2 ) ) ] , α + = 1 2 d Δ t h δ ω + i / T 2 ( d E 0 ) 2 1 δ ω + i / T 1 ( i T 2 + 1 δ ω + i / T 2 ) , α = α + + | δ ω δ ω , α + = α + | δ ω δ ω ,
Δ ω pull ( β GVD ) = c δ ω 2 β GVD n ( ω 0 ) + 1 2 c ω 0 β GVD
g κ d ω 0 c 2 2 n 2 ( ω 0 ) [ α + + α + ] .
δ ω 2 = d | E 0 | 1 T 2 T g 1 T g 2 .

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